Vector Quantization Scalar Quantization Scalar Quantization v s
- Slides: 25
矢量量化 (Vector Quantization) 赵胜辉
Scalar Quantization
Scalar Quantization v. s. Vector Quantization
Why VQ? x 2 x 1
Why VQ?
Why VQ? • Memory advantage – Dependency between input samples – Vanishes if the input samples are independent • Shape advantage – Better adaptation of VQ quantization point density to the PDF of input – Vanishes in the case of entropy-constrained quantization • Space-filling advantage – Greater freedom of VQ in selecting quantization cell shapes – The advantage of an infinite-dimension VQ is 0. 255 bits per dimension for the squared-error distortion
How to do VQ? • S. P. Lloyd, “Least squares quantization in PCM, ” IEEE Trans. Inform. Theory, vol. IT-28, pp. 129 -137, 1982 – Lloyd algorithm (k-means algorithm) Generalized Lloyd algorithm (GLA) • Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design, ” IEEE Trans. Comm. , vol. COM-28, pp. 84 -95, 1980 • An iterative method that guarantee only local optimality
How to do VQ? • Two optimality conditions – Optimizing the encoder 最近邻准则 – Optimizing the decoder Yi = argmin E[d(X, Z)︱X∈Vi ] Z ∈Rk Yi = E[X︱X∈Vi ] Yi = 1/Ni ∑X X∈Vi k-means
Discrete GLA
Some implementation problems • Large computational complexity due to the exhaustive codebook searching • Codebook storage • Large computational complexity due to codebook training Dimension (codeword length) Codebook size The size of training data
Structured VQ • • • Tree-structured VQ Multi-stage VQ Split VQ Gain-Shape VQ Mean-Removed VQ
Tree-structured VQ
Multi-stage VQ
Split VQ X 1: (x 1, x 2, x 3, x 4) X: (x 1, x 2, x 3, …, x 8) X 2: (x 5, x 6, x 7, x 8)
Gain-Shape VQ
Mean-Removed VQ Mean vector codebook + Mean-removed vector codebook
Rate-constrained VQ vs. Entropy-Constrained VQ • The optimal quantizer means minimizing the average distortion. • The resolution constraint limits the size of the codebook, i. e. , fixed-rate. • The entropy constraint limits the entropy for the quantization indices, i. e. , variable-rate.
- Scalar and vector quantization
- Vector quantization
- Angular displacement scalar or vector
- Dot product glm
- Hasil kali dua vektor
- Vector vs scalar quantities
- Dot
- Vector vs scalar examples
- A scalar quantity has
- Scalar and vector projections
- 80cos30
- Characteristics of vector quantity
- Vector vs scalar
- Scalar vs vector
- Moment of couple formula
- Vector vs scalar
- Scalar and vector quantity difference
- Scalar vector tensor
- Tensor order
- Scalar vs vector
- Teco manuals
- Distance scalar
- Venn diagram of a union b
- Scalar pipeline vs superscalar pipeline
- Components of a vector
- Centripetal force scalar or vector